take the sine of both sides

what y value will make this true? (look at your unit circle)

take cosecant of both sides

convert to sine notation

What value of y makes this true? look at your unit circle, note that 1/sqrt(2) is the same as sqrt(2)/2

remember that arctangent is an angle, it is the angle that when you take the tangent of it, you will get negative one.

So draw a right triangle, and mark the opposite side as -1, and the adjacent side as 1. Then use the Pythagorean theorem to mark the hypotenuse sqrt(2)

This triangle is the triangle that if you took the tangent of it, you would get -1, so it is the triangle represented by tan^-1(-1)

Now we want the sine of this triangle, so that will be opposite over hypotenuse, which gives us -1/sqrt(2)